Multi-Objective Genetic Algorithms for the Single Allocation Hub Location Problem

Hub Location Problems play vital economic roles in transportation and telecommunication networks where goods or people must be efficiently transferred from an origin to a destination point whilst direct origin-destination links are impractical. This work investigates the single allocation hub location problem, and proposes a genetic algorithm (GA) approach for it. The effectiveness of using a single-objective criterion measure for the problem is ���rst explored. Next, a multi-objective GA employing various ���tness evaluation strategies such as Pareto ranking, sum of ranks, and weighted sum strategies is presented. The effectiveness of the multi-objective GA is shown by comparison with an Integer Programming strategy, the only other multi-objective approach found in the literature for this problem. Lastly, two new crossover operators are proposed and an empirical study is done using small to large problem instances of the Civil Aeronautics Board (CAB) and Australian Post (AP) data sets.

Using genetic algorithms for the single allocation hub location problem

Hub location problem is an NP-hard problem that frequently arises in the design of transportation and distribution systems, postal delivery networks, and airline passenger flow. This work focuses on the Single Allocation Hub Location Problem (SAHLP). Genetic Algorithms (GAs) for the capacitated and uncapacitated variants of the SAHLP based on new chromosome representations and crossover operators are explored. The GAs is tested on two well-known sets of real-world problems with up to 200 nodes. The obtained results are very promising. For most of the test problems the GA obtains improved or best-known solutions and the computational time remains low. The proposed GAs can easily be extended to other variants of location problems arising in network design planning in transportation systems.

A Multi-Objective Genetic Algorithm with Side Effect Machines for Motif Discovery

Understanding the machinery of gene regulation to control gene expression has been one of the main focuses of bioinformaticians for years. We use a multi-objective genetic algorithm to evolve a specialized version of side effect machines for degenerate motif discovery. We compare some suggested objectives for the motifs they find, test different multi-objective scoring schemes and probabilistic models for the background sequence models and report our results on a synthetic dataset and some biological benchmarking suites. We conclude with a comparison of our algorithm with some widely used motif discovery algorithms in the literature and suggest future directions for research in this area.

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

Characterizing Dynamic Optimization Benchmarks for the Comparison of Multi-Modal Tracking Algorithms

Population-based metaheuristics, such as particle swarm optimization (PSO), have been employed to solve many real-world optimization problems. Although it is of- ten sufficient to find a single solution to these problems, there does exist those cases where identifying multiple, diverse solutions can be beneficial or even required. Some of these problems are further complicated by a change in their objective function over time. This type of optimization is referred to as dynamic, multi-modal optimization. Algorithms which exploit multiple optima in a search space are identified as niching algorithms. Although numerous dynamic, niching algorithms have been developed, their performance is often measured solely on their ability to find a single, global optimum. Furthermore, the comparisons often use synthetic benchmarks whose landscape characteristics are generally limited and unknown. This thesis provides a landscape analysis of the dynamic benchmark functions commonly developed for multi-modal optimization. The benchmark analysis results reveal that the mechanisms responsible for dynamism in the current dynamic bench- marks do not significantly affect landscape features, thus suggesting a lack of representation for problems whose landscape features vary over time. This analysis is used in a comparison of current niching algorithms to identify the effects that specific landscape features have on niching performance. Two performance metrics are proposed to measure both the scalability and accuracy of the niching algorithms. The algorithm comparison results demonstrate the algorithms best suited for a variety of dynamic environments. This comparison also examines each of the algorithms in terms of their niching behaviours and analyzing the range and trade-off between scalability and accuracy when tuning the algorithms respective parameters. These results contribute to the understanding of current niching techniques as well as the problem features that ultimately dictate their success.

A Scalability Study and New Algorithms for Large-Scale Many-Objective Optimization

Many real-world optimization problems contain multiple (often conflicting) goals to be optimized concurrently, commonly referred to as multi-objective problems (MOPs). Over the past few decades, a plethora of multi-objective algorithms have been proposed, often tested on MOPs possessing two or three objectives. Unfortunately, when tasked with solving MOPs with four or more objectives, referred to as many-objective problems (MaOPs), a large majority of optimizers experience significant performance degradation. The downfall of these optimizers is that simultaneously maintaining a well-spread set of solutions along with appropriate selection pressure to converge becomes difficult as the number of objectives increase. This difficulty is further compounded for large-scale MaOPs, i.e., MaOPs possessing large amounts of decision variables. In this thesis, we explore the challenges of many-objective optimization and propose three new promising algorithms designed to efficiently solve MaOPs. Experimental results demonstrate the proposed optimizers to perform very well, often outperforming state-of-the-art many-objective algorithms.

Enabling and Measuring Complexity in Evolving Designs using Generative Representations for Artificial Architecture

As the complexity of evolutionary design problems grow, so too must the quality of solutions scale to that complexity. In this research, we develop a genetic programming system with individuals encoded as tree-based generative representations to address scalability. This system is capable of multi-objective evaluation using a ranked sum scoring strategy. We examine Hornby's features and measures of modularity, reuse and hierarchy in evolutionary design problems. Experiments are carried out, using the system to generate three-dimensional forms, and analyses of feature characteristics such as modularity, reuse and hierarchy were performed. This work expands on that of Hornby's, by examining a new and more difficult problem domain. The results from these experiments show that individuals encoded with those three features performed best overall. It is also seen, that the measures of complexity conform to the results of Hornby. Moving forward with only this best performing encoding, the system was applied to the generation of three-dimensional external building architecture. One objective considered was passive solar performance, in which the system was challenged with generating forms that optimize exposure to the Sun. The results from these and other experiments satisfied the requirements. The system was shown to scale well to the architectural problems studied.

Generating Aesthetically Pleasing Images in a Virtual Environment using Particle Swarm Optimization

This research focuses on generating aesthetically pleasing images in virtual environments using the particle swarm optimization (PSO) algorithm. The PSO is a stochastic population based search algorithm that is inspired by the flocking behavior of birds. In this research, we implement swarms of cameras flying through a virtual world in search of an image that is aesthetically pleasing. Virtual world exploration using particle swarm optimization is considered to be a new research area and is of interest to both the scientific and artistic communities. Aesthetic rules such as rule of thirds, subject matter, colour similarity and horizon line are all analyzed together as a multi-objective problem to analyze and solve with rendered images. A new multi-objective PSO algorithm, the sum of ranks PSO, is introduced. It is empirically compared to other single-objective and multi-objective swarm algorithms. An advantage of the sum of ranks PSO is that it is useful for solving high-dimensional problems within the context of this research. Throughout many experiments, we show that our approach is capable of automatically producing images satisfying a variety of supplied aesthetic criteria.

Automatic Structure Generation using Genetic Programming and Fractal Geometry

Three dimensional model design is a well-known and studied field, with numerous real-world applications. However, the manual construction of these models can often be time-consuming to the average user, despite the advantages o ffered through computational advances. This thesis presents an approach to the design of 3D structures using evolutionary computation and L-systems, which involves the automated production of such designs using a strict set of fitness functions. These functions focus on the geometric properties of the models produced, as well as their quantifiable aesthetic value - a topic which has not been widely investigated with respect to 3D models. New extensions to existing aesthetic measures are discussed and implemented in the presented system in order to produce designs which are visually pleasing. The system itself facilitates the construction of models requiring minimal user initialization and no user-based feedback throughout the evolutionary cycle. The genetic programming evolved models are shown to satisfy multiple criteria, conveying a relationship between their assigned aesthetic value and their perceived aesthetic value. Exploration into the applicability and e ffectiveness of a multi-objective approach to the problem is also presented, with a focus on both performance and visual results. Although subjective, these results o er insight into future applications and study in the fi eld of computational aesthetics and automated structure design.

Automatic evolution of conceptual building architectures

This thesis describes research in which genetic programming is used to automatically evolve shape grammars that construct three dimensional models of possible external building architectures. A completely automated fitness function is used, which evaluates the three dimensional building models according to different geometric properties such as surface normals, height, building footprint, and more. In order to evaluate the buildings on the different criteria, a multi-objective fitness function is used. The results obtained from the automated system were successful in satisfying the multiple objective criteria as well as creating interesting and unique designs that a human-aided system might not discover. In this study of evolutionary design, the architectures created are not meant to be fully functional and structurally sound blueprints for constructing a building, but are meant to be inspirational ideas for possible architectural designs. The evolved models are applicable for today's architectural industries as well as in the video game and movie industries. Many new avenues for future work have also been discovered and highlighted.

Genetic Programming for Non-Photorealistic Rendering

This thesis focuses on developing an evolutionary art system using genetic programming. The main goal is to produce new forms of evolutionary art that filter existing images into new non-photorealistic (NPR) styles, by obtaining images that look like traditional media such as watercolor or pencil, as well as brand new effects. The approach permits GP to generate creative forms of NPR results. The GP language is extended with different techniques and methods inspired from NPR research such as colour mixing expressions, image processing filters and painting algorithm. Colour mixing is a major new contribution, as it enables many familiar and innovative NPR effects to arise. Another major innovation is that many GP functions process the canvas (rendered image), while is dynamically changing. Automatic fitness scoring uses aesthetic evaluation models and statistical analysis, and multi-objective fitness evaluation is used. Results showed a variety of NPR effects, as well as new, creative possibilities.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Disease-Gene Association Using a Genetic Algorithm

Understanding the relationship between genetic diseases and the genes associated with them is an important problem regarding human health. The vast amount of data created from a large number of high-throughput experiments performed in the last few years has resulted in an unprecedented growth in computational methods to tackle the disease gene association problem. Nowadays, it is clear that a genetic disease is not a consequence of a defect in a single gene. Instead, the disease phenotype is a reflection of various genetic components interacting in a complex network. In fact, genetic diseases, like any other phenotype, occur as a result of various genes working in sync with each other in a single or several biological module(s). Using a genetic algorithm, our method tries to evolve communities containing the set of potential disease genes likely to be involved in a given genetic disease. Having a set of known disease genes, we first obtain a protein-protein interaction (PPI) network containing all the known disease genes. All the other genes inside the procured PPI network are then considered as candidate disease genes as they lie in the vicinity of the known disease genes in the network. Our method attempts to find communities of potential disease genes strongly working with one another and with the set of known disease genes. As a proof of concept, we tested our approach on 16 breast cancer genes and 15 Parkinson's Disease genes. We obtained comparable or better results than CIPHER, ENDEAVOUR and GPEC, three of the most reliable and frequently used disease-gene ranking frameworks.

Object-Oriented Genetic Programming for the Automatic Inference of Graph Models for Complex Networks

Complex networks are systems of entities that are interconnected through meaningful relationships. The result of the relations between entities forms a structure that has a statistical complexity that is not formed by random chance. In the study of complex networks, many graph models have been proposed to model the behaviours observed. However, constructing graph models manually is tedious and problematic. Many of the models proposed in the literature have been cited as having inaccuracies with respect to the complex networks they represent. However, recently, an approach that automates the inference of graph models was proposed by Bailey [10] The proposed methodology employs genetic programming (GP) to produce graph models that approximate various properties of an exemplary graph of a targeted complex network. However, there is a great deal already known about complex networks, in general, and often specific knowledge is held about the network being modelled. The knowledge, albeit incomplete, is important in constructing a graph model. However it is difficult to incorporate such knowledge using existing GP techniques. Thus, this thesis proposes a novel GP system which can incorporate incomplete expert knowledge that assists in the evolution of a graph model. Inspired by existing graph models, an abstract graph model was developed to serve as an embryo for inferring graph models of some complex networks. The GP system and abstract model were used to reproduce well-known graph models. The results indicated that the system was able to evolve models that produced networks that had structural similarities to the networks generated by the respective target models.